The Reds were thumped 4-0, with Mohamed Salah missing from the penalty spot.
Van Dijk said afterwards: "Very difficult - very difficult to accept, very difficult to be out there. Very tough day and I feel bad for the fans as well.
"All the responsibility, we are the ones not performing on the pitch. We know how the world works. We have to stick together, even how difficult that is. It’s just a big blow that we’re out of the FA Cup because up until the penalty I don’t think there were any issues."
The defender added, "I can understand that (supporters leaving before full-time). Obviously they have been going through ups and downs, like we obviously have as well.
"Obviously we would love them to be staying up until the end but if you’re 4-0 down and the way we played second half then I can understand the anger. In my time at Liverpool we have been going through tough times and at the moment it’s a tricky one as well.